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On the repeated volunteer’s dilemma with equal cost sharing
Journal article   Open access   Peer reviewed

On the repeated volunteer’s dilemma with equal cost sharing

Rabah Amir, Huizhong Liu, Tatiana Mayskaya and Jingwen Tian
Economic theory
07/30/2026
DOI: 10.1007/s00199-026-01735-y
Appears in  UI Libraries Support Open Access
url
https://doi.org/10.1007/s00199-026-01735-yView
Published (Version of record) Open Access

Abstract

We study the symmetric volunteer’s dilemma with binary actions and cost sharing, where the volunteering cost is split equally among volunteers. In the one-shot game, all pure-strategy Nash equilibria involve a single volunteer, while Pareto optimality allows any non-zero number. In the infinitely repeated game, all Pareto optima can be sustained in a subgame-perfect Nash equilibrium based on a grim-trigger strategy: trivially under undiscounted payoffs, and provided the discount factor exceeds a threshold under discounted payoffs. This threshold is non-monotonic in the number of volunteers; it is zero with one volunteer, highest with two, and decreases with both more volunteers beyond two and more players. Thus, the scope for tacit cooperation is universal with one volunteer, minimal with two, then improving as more join in, all the way to universal again only in the limit with more and more players and volunteers. Considering efficiency, scope for cooperation and equity/focality as criteria, the grand coalition of volunteers emerges as the best cooperation scenario.
 Coalition formation Cost sharing Pareto optimality Repeated games Volunteer’s dilemma UIOWA OA Agreement

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